Does that mean it is redundant to add umami (such as monosodium glutamate) or soy based flavorings to tomato-based sauces, or is there a benefit?

For example, a typical tomato-based sauce is cocktail sauce, which often has worcestershire sauce in it as an ingredient. However, the main active component of worcestershire sauce is fermented fish sauce or soy, which is primarily valued for its umami. So, if umami is already present in the tomatoes, why add the worcestershire at all?

I had to look up cocktail sauce, as it's not something I'd ever heard of in the UK. For the benefit of others, could you link in your favourite recipe, or some simple construction details [I know it's not difficult having just researched it, but it may help future visitors who are not US-based]
– TetsujinJan 4 '19 at 16:06

MSG can make products delicious, but you can take it too far...sometimes dishes begin tasting like dashi.
– moscafjJan 4 '19 at 20:41

4 Answers
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The Wikipedia article you link actually hints at an answer. It points out that there's a synergistic effect when combining different classes of umami-rich foods, leading to a greater flavour enhancement than would be expected simply by adding the effects of the ingredients

Japanese make dashi with kombu seaweed and dried bonito flakes;... and Italians combine Parmesan cheese on tomato sauce with mushrooms.

So it's certainly traditional. But in your example the tomatoes bring some sweetness along with the umami, while the Worcester sauce (like soy sauce) is salty and so rich in umami it's used in small quantities. The effect of combining them is a more savoury sauce than one that tried to get all its umami from tomatoes. Red pesto uses parmesan to similar effect.

If you're only looking for umami, then it's potentially redundant. But looking at the bigger picture, we add other ingredients to round out the overall flavor. Using solely tomato can be too plain / sweet / sour.

There is also a strong school of thought that says partial matching of flavor profiles helps when looking for flavor balance. Say you are starting with a tomato base that is providing umami and sour and you want to boost sweet, salt and heat. You could just add some hot sauce, salt and sugar and say you are balanced. But if your source matched umami, it may very well blend better into a more satisfying balance. It would only be a redundant flavor if it started to dominate in that case. So, in your cocktail sauce example, you might not want to use acid as you matching profile because you may push to the point of sour being too dominant.